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09 July 2020
 
  » arxiv » 1204.3009

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Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation
Lauri Toikka ; Jarmo Hietarinta ; Kalle-Antti Suominen ;
Date 13 Apr 2012
AbstractWe construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlev’e transcendent. In each case the potential can be chosen to be time-independent.
Source arXiv, 1204.3009
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